Agree on getting enough protein (and sleep, and recovery time).
Strength training isn't all about mass. You can get stronger without gaining mass. There is a neural component and an efficiency component. At some point though you do need a bigger muscle to be stronger. There is also the question of whether you're optimizing for faster (fast twitch) or slower movements.
Strength training is not only about mass but for most intents and purposes it is about gaining as much muscle as possible while not gaining too much extra.
It's not like one can move from squating 100kg to squating 150kg without extra 2-3 kgs of meat.
And there is NO WAY of growing meat in a calorie deficit. And running often leads to that.